<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Hypergeometric 2F0</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../hypergeometric.html" title="Hypergeometric Functions">
<link rel="prev" href="hypergeometric_0f1.html" title="Hypergeometric 0F1">
<link rel="next" href="hypergeometric_1f1.html" title="Hypergeometric 1F1">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="hypergeometric_0f1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_1f1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.hypergeometric.hypergeometric_2f0"></a><a class="link" href="hypergeometric_2f0.html" title="Hypergeometric 2F0">Hypergeometric
      <sub>2</sub><span class="emphasis"><em>F</em></span><sub>0</sub></a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">hypergeometric_2F0</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">);</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>

<span class="special">}}</span>
</pre>
<h5>
<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h0"></a>
        <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.description"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.description">Description</a>
      </h5>
<p>
        The function <code class="computeroutput"><span class="identifier">hypergeometric_2F0</span></code>
        returns the result of
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0.svg"></span>

        </p></blockquote></div>
<p>
        The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
        type calculation rules</em></span></a> when <code class="computeroutput"><span class="identifier">T1</span></code>
        and <code class="computeroutput"><span class="identifier">T2</span></code> are different types.
      </p>
<p>
        The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
        be used to control the behaviour of the function: how it handles errors,
        what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy
        documentation for more details</a>.
      </p>
<p>
        The functions return the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
        whenever the result is undefined or complex. The valid domain for this function
        occurs only when one of <code class="computeroutput"><span class="identifier">a1</span></code>
        or <code class="computeroutput"><span class="identifier">a2</span></code> is a negative integer:
        ie the polynomial case.
      </p>
<h5>
<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h1"></a>
        <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.implementation"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.implementation">Implementation</a>
      </h5>
<p>
        When <code class="computeroutput"><span class="identifier">a1</span> <span class="special">==</span>
        <span class="identifier">a2</span> <span class="special">-</span>
        <span class="number">0.5</span></code> then the function is implemented
        in terms of the Hermite polynomial:
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_hermite.svg"></span>

        </p></blockquote></div>
<p>
        When both <code class="computeroutput"><span class="identifier">a1</span></code> and <code class="computeroutput"><span class="identifier">a2</span></code> are integers then the function is implemented
        in terms of the associated-Laguerre polynomial:
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_laguerre.svg"></span>

        </p></blockquote></div>
<p>
        If the defining series is divergent, we use the continued fraction
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_cf.svg"></span>

        </p></blockquote></div>
<p>
        Otherwise we use the defining series.
      </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="hypergeometric_0f1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_1f1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
